Difference between revisions of "Extras"

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[[Category:Cosmic Microwave Background (CMB)|6]]
 
[[Category:Cosmic Microwave Background (CMB)|6]]
=Extras=
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<div id="cmb2"></div>
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<div style="border: 1px solid #AAA; padding:5px;">
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=== Problem 1 ===
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In year 1953 the article "Extended Universe and creation of Galactics" by G.A. Gamov was published.<br/>
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In that paper Gamov took two numbers - the age of the world and average density of matter in the Universe - and basing on them he determined the third number: the temperature of the relic radiation (cosmic microwave background). Try to repeat the scientific feat of Gamov.
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  <div class="NavHead">solution</div>
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    <p style="text-align: left;">Gamov considered the simplest variant of cosmological dynamics---the inertial regime of the expansion of Universe: \( R \propto t,\ v = const.
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\) Density of homogeneous Universe, filled by non-relativistic matter, is
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\[
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\rho _m  = \frac{M}{{(4/3\pi )R^3 }} = \rho _m (t_0 )\left(
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{\frac{{t_0 }}{t}} \right)^3.
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\]
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Gamov used the following numerical numbers for current age of Universe and the matter density respectively:
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\( t_0  \simeq 3\cdot^10^9\mbox{years},
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\rho _m (t_0 ) \simeq 10^{-30} \mbox{\it g/cm}^3.\) Energy density in the radiation dominated Universe is
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\[
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\rho _r  = \frac{3}{{32\pi Gt^2 }}.
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\]
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Then Gamov used the condition $\rho _r (t^*) = \rho _m (t^*)$ to find the moment of time when radiation-dominated epoch changed to matter-dominated one:
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\(
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t^*  \simeq 73\cdot10^6\ \mbox{years}\) Then he made use of the Stephan-Boltzmann law to determine the temperature in the joining point, i.e. at the time moment $t^*$ , \( T(t^*) = 320K.\) It is left only to use the condition $aT = const,$ in order to convert the temperature for the present time to obtain the following
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\[
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T(t_0 ) = T\left( {t^*} \right){\frac{{t^*}}{{t_0 }}}  \simeq 7K.
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\]
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"Is it possible to take two asymptotes, join them and determine the CMB temperature? The answer is, firstly, it is impossible, and secondly, Gamov did it already long ago." (A.D. Chernin)</p>
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Revision as of 21:24, 1 October 2012



Problem 1

In year 1953 the article "Extended Universe and creation of Galactics" by G.A. Gamov was published.
In that paper Gamov took two numbers - the age of the world and average density of matter in the Universe - and basing on them he determined the third number: the temperature of the relic radiation (cosmic microwave background). Try to repeat the scientific feat of Gamov.